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2 years ago

Please help me solve for x

Mathematics

1 answer:

andreev551 [17]2 years ago

5 0

Answer:

x=9

Step-by-step explanation:

Corresponding angles are equal

7x - 3 = 60

7x. = 63

÷7

x = 9

Check:

7x9 - 3 = 60

Hope this helps!

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Identify any extrema of the function by recognizing its given form or its form after completing the square. Verify your results

Andrews [41]

Answer:

Step-by-step explanation:

Given that,

g(x, y) = 5 - (x - 3)² - (y + 2)²

Let find the grad of the function,

The grad of a function is defined as

∇g= ∂g/∂x •i + ∂g/∂y •j + ∂g/∂z •k

∇g = gx•i + gy•j + gz•k

gx = -2(x-3) = -2x+6

gy = -2(y+2) = -2y -4

∇g = (-2x+6) •i + (-2y-4)•j

We have a maximum or a minimum If g conservative, then, ∇g = 0i +0j

Then comparing this to the grad of the function

(-2x+6) •i + (-2y-4)•j = 0i +0j

Then, -2x+6 = 0

2x=6

x = 3

Also, -2y-4=0

-2y=4

y = -2

Then, g(x, y) = 5 - (x - 3)² - (y + 2)²

g(x, y) = 5 - (3 - 3)² - (-2 + 2)²

g(x, y) = 5

So the critical point is (3, -2, 5)

gx =-2x+6

Second derivative of gx with respect to x

gxx=-2

gy=-2y-4

Second derivative of gy with respect to y

gyy=-2

Second derivative of gx with respect to y

gxy =0

d =gxxgyy - (gxy)²

Then, gyy=gxx

d = -2×-2 -0²

d = 4-0=4

Since d>0

Since d is greater than 0, then, it is not a chair points.

Then, since gxx=-2<0, gyy=-2<0

Cause the second derivative in x (or in y) is less than zero, then the point is relatively maximum

So the maximum point is (3, -2, 5).

6 0

2 years ago

* The nth term of sequence A is 3n − 2 The nth term of sequence B is 10 − 2n Sally says there is only one number that is in both

Nina [5.8K]

Answer:

Sally is not right

Step-by-step explanation:

Given the two sequences which have their respective $n^{th}$ terms as following:

Sequence A. $3n - 2$

Sequence B. $10 - 2n$

As per Sally, there exists only one number which is in both the sequences.

To find:

Whether Sally is correct or not.

Solution:

For Sally to be correct, we need to put the $n^{th}$ terms of the respective sequences as equal and let us verify that.

$3n-2=10-2n\\\Rightarrow 3n+2n=10+2\\\Rightarrow 5n=12\\\Rightarrow n = \dfrac{12}{5}$

When we talk about $n^{th}$ terms, $n$ here is a whole number not a fractional number.

But as per the statement as stated by Sally $n$ is a fractional number, only then the two sequences can have a number which is in the both sequences.

Therefore, no number can be in both the sequences A and B.

Hence, Sally is not right.

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2 years ago

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Nady [450]

Answer:

y=6x+20

Step-by-step explanation:

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3 years ago

A car drvies at a speed of 60 mph for 30 minutes. Calculate how far it travles

Studentka2010 [4]

Answer:

30 miles

Step-by-step explanation:

Distance = speed x time

30 minutes can be considered as ½ an hour.

60 x ½=30miles

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2 years ago

H(x) = -x - 1, find h(-2)

eduard

Answer:

I think the answer is 1

Step-by-step explanation:

-(-2)-1

6 0

2 years ago